204 
ME. A. CAYLEY ON THE DOUBLE TANGENTS OE A PLANE CTEYE, 
and the identical equation is 
Ia+II54-nic+IV(^=0, 
where 
1= 
d, 
y 
9 
d. 
c, 
d 
c\ 
y. 
W 
II-- 
c, 
h. 
a! 
— 
c, 
a , 
y 
d. 
c, 
y 
d, 
d 
c\ 
y, 
a!' 
c', 
d. 
y 
III=- 
a. 
h, 
y 
— 
a. 
c, 
d , 
5, 
c, 
d 
d. 
y 
a!. 
y, 
W 
c', 
d' 
IV = 
a. 
b, 
d 
5 
c, 
y 
a'. 
y, 
d' 
or, as we may express them, 
1 = 
a{ 0 
+ b{ d^ ) 
(12) 
-\-c{y'c—yd—dy) 
(13) 
^d{-yh-^yy ) 
(14) 
11= a{ -d^ 
) 
(21) 
+ 5( 0 
) 
+ c ( — d'c — y'i -^-dd df-yV-^-di 
d) 
(23) 
-\-d{ d’i-\-ya-dy-yd 
) 
(24) 
iii= a{—yc-\-yd-\-dy 
) 
(31) 
+ h{ d'c-\-yh — dd — yy ~ dd) 
(32) 
+ c( 0 
) 
-\-d{-~ad’ ■\-d^ 
) 
(34) 
IV = a{y''b —yy 
) 
(41) 
-f J ( — d'h — ya-\-dy + yd 
) 
(42) 
+c( d’a —dd 
) 
(43) 
+ 0 ) • 
which verify the identical equation. We have III= — A"DH, IV = A'H, 
II=+A"J3i^, I= — A"i|, and thence the equation in question, 
-l^.U+il3l.DU-iDH.J3T+H.T=0. 
